Algebraic Geometry Seminar
Wednesday, April 21, 2004, 4:00pm, 120 Physics
Craig Grabowski (Duke University)
1-Cycles on Abelian 3-Folds

Abstract:

Abstract : The goal of this talk is to show that, for complex abelian varieties of dimension 3, all integral classes of Hodge type (2,2) come from algebraic 1-cycles, or integer linear combinations of curves on the abelian variety. As a result, abelian 3-folds satisfy an integral version of the Hodge conjecture, which states that all rational cohomology classes of type (n-k,n-k) come from algebraic k-cycles after tensoring with the rationals.

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